Question 1

What is the range of cos⁻¹(x)?

Accepted Answer

[0, π]

Answer

[−π, π]

Answer

(−∞, ∞)

Answer

[−π/2, π/2]

Question 2

What does the 'principal value' mean in inverse trigonometric functions?

Accepted Answer

The main value of the function within its restricted range

Answer

The average of all possible values

Answer

The sum of all angles in a unit circle

Answer

The smallest possible angle

Question 3

What statement best describes the relationship between a trigonometric function and its inverse?

Accepted Answer

They cancel or undo each other

Answer

They are unrelated functions

Answer

They are identical in shape and period

Answer

They both repeat infinitely

Question 4

If sin⁻¹(x) = θ, then what does sin(θ) equal?

Accepted Answer

x

Answer

θ

Answer

Undefined

Answer

1/x

Question 5

Which inverse function graph passes through the origin?

Accepted Answer

Both B and C

Answer

y = tan⁻¹(x)

Answer

y = sin⁻¹(x)

Answer

y = cos⁻¹(x)

Question 6

How does restricting the range make trigonometric functions invertible?

Accepted Answer

It limits them to one output per input

Answer

It makes them periodic

Answer

It increases their amplitude

Answer

It makes them increase faster

Question 7

Are inverse trigonometric functions periodic?

Accepted Answer

No, they are not periodic

Answer

Yes, all of them are

Answer

Only tan⁻¹(x)

Answer

Only sin⁻¹(x)

Question 8

A student claims that the range of tan⁻¹(x) is [0, π]. Is this correct?

Accepted Answer

No, it is (−π/2, π/2)

Answer

No, it is [0, 2π]

Answer

Yes

Answer

No, it is [−π, π]

Question 9

What is the principal value of sin⁻¹(0)?

Accepted Answer

0

Answer

Undefined

Answer

π

Answer

π/2

Question 10

What is the range of tan⁻¹(x)?

Accepted Answer

(−π/2, π/2)

Answer

[−1, 1]

Answer

(0, π)

Answer

(−π, π)

Question 11

Is tan⁻¹(√3) undefined?

Accepted Answer

No, it equals π/3

Answer

Yes, because √3 > 1

Answer

No, it equals π/2

Answer

Yes

Question 12

Is tan⁻¹(x) periodic?

Accepted Answer

No

Answer

Sometimes

Answer

Only for small x

Answer

Yes

Question 13

What is the value of sin⁻¹(√3/2)?

Accepted Answer

π/3

Answer

π/2

Answer

π/4

Answer

π/6

Question 14

What is the value of sin⁻¹(−1)?

Accepted Answer

−π/2

Answer

Undefined

Answer

0

Answer

π/2

Question 15

How do y = sin⁻¹(x) and y = tan⁻¹(x) differ in domain?

Accepted Answer

sin⁻¹(x) is [−1, 1], tan⁻¹(x) is (−∞, ∞)

Answer

tan⁻¹(x) is [−1, 1], sin⁻¹(x) is all real numbers

Answer

sin⁻¹(x) is all real numbers, tan⁻¹(x) is not

Answer

They have the same domain

Related quizzes

Related quizzes